vktamhane12@rediffmail.com (V.K.Tamhane) wrote in message news:<9d62a326.0408100051.37a3eca4@posting.google.com>...
> selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:<a42650fc.0408080626.27047097@posting.google.com>...
> > vktamhane12@rediffmail.com (V.K.Tamhane) wrote in message news:<9d62a326.0407170443.5990dad7@posting.google.com>...
> > > selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:<a42650fc.0407161931.376c92f0@posting.google.com>...
> > > > "Spaceman" <Spaceman@realspaceman.com> wrote in message news:<VLZIc.65325$JR4.14174@attbi_s54>...
[snip]

> 
>      Sorry for the delay in replying- on account of my pre-occupation.
> Mathematics is now correct and it is a good example, which shows that
> difference in the motional and induced emf cannot be separated
> mathematically, even if non-homogeneous magnetic fields are
> considered. Your further arguments are of course correct and it is a
> good paper.
>      May I draw the conclusion? Mathematics is just a tool for
> calculations and excellent at that but physical phenomenon is
> independent of any formula. It is for this reason that the concepts
> and mechanisms are important in physics. Not to calculate results but
> to actually understand the physics itself.
>      You have taken great efforts to prove the basic and fundamental
> mechanisms and certainly differentiated between the two actions
> responsible for the magnetic field based electromotive force.

Dear Mr Tamhane, how exactly you noted the connection between the
mathematical and physical formalism in comprehension of deep
underpinning of processes in nature. I from my side can only add that
the mathematical formalism can be true even with some incorrect
phenomenology. We see many examples in today physics based on the
principle properly formulated by Feynman: "Philosophers try to tell of
the nature without mathematics. I try to describe the nature
mathematically".

So it happens: if, for example, we do not penetrate into the physics,
how EM excitation is passed, and represent the light as some particles
- photons, then in some area of revelations we will be quite able to
find a definite analogy with the observed phenomena and even to build
quite harmonious mathematical formalism. However, all this formalism
will be workable only in limits of phenomena on whose basis it was
built. A step to the left either right - and the whole formalism
fails. On the other hand, the grasp of failing formalism out of the
area where it is true forms the dogmatism and its direct consequence -
the crisis in science, which several generations of scientists so hard
and heroically surmount.

We encounter such cases at every step. For example, in the circuit
theory, colleagues have persuaded themselves that two-port theory is
absolutely true; they do not want to see that in its very essence it
is inapplicable to mismatched ladder filters. They do not care that
their calculations are irrelevant to the experimental results. They
care only to be correct in their secondary mathematical
transformations and shut their eyes to everything other.

The same in mechanics. The specialists run in hurry to calculate
nonlinear vibrations, having not solved rigorously and in full amount
the problems of linear dynamics. I show them that the solutions on
which they rely are essentially incomplete; I show that in Kirhgoff
mathematical model the general differential equation and initial and
boundary conditions are superfluous, because the initial conditions
are given by the external force and boundary conditions have been
already used in the very differential equation. Colleagues "do not
understand" this, as they rely on mathematical formalism as such, they
threw away the limitations which the authors of conceptions initially
introduced - and live in their virtual world of attractors and
fractals feeling happy of complicated mathematics.

The same we see in astronomy. They like the theories of black holes,
Doppler substantiation of red shift, galaxy cannibalism - and no one
cares now that no astronomic observation evidences them clearly. No
one cares to deepen their understanding of physics of processes. They
are happy of abstract mathematical modelling based not on the physics
but on convenient fantasies.

The difficulty is here that we can easily deceive the mathematics. It
is enough to introduce convenient laws and postulates in the statement
of problem, then the mathematics will flow in usual fully harmonious
way. And only the physics is able to show the math incorrect,
comparing the result with experiment.

On the other hand, the physics without mathematics loses its sense,
too, as mathematics reveals the structure of many links which are
difficult to be seen mentally. We often encountered such difficulty
that some colleagues, having built a merely mental conception, did not
take into account some outwardly negligible regularities which could
be revealed only mathematically. With it, in description of process
they automatically did not account some important nuances, usually
connected with resonance phenomena. In this way merely mental
conceptions are doomed to be incorrect.

And the more complicated are phenomena with which we deal the more
responsibility they put on us we to model these processes
comprehensively and correctly and to provide the complete description
of their pattern. Partially this is reflected in our paper to which
you responded so favourably. As far as we see, in this paper we raised
more questions than provided solutions. And this is quite objectively.
In EM induction phenomenology we still have too many unstudied
aspects, in particular I mean the difference in motional and induced
emf, as you so correctly emphasised. Actually, permanent magnetic
field does not deliver work, and time-variable does - this is a very
old question raised by Ampere in his unsuccessful attempts to reveal
the induction in permanent magnetic field. As far as we could, we
showed that out of understanding the essence of the induction process,
it is impossible to formulate the fully correct field equations. And
here the standard trick of physics - to postulate the phenomenon -
cannot be of help. The postulation will not enable us to leave the
limits of postulation itself, just as the vector representation
through the flux of vector disables us to see the process itself in
all its diversity and revelations. We think, it is a great problem and
one of paramount problems in the field theory.

The second no less important problem is, standard modelling equations
of fields have been built on the basis of vector analysis developed
for stationary fields. And this concerns not only Maxwell theory but
also hydrodynamics. In our papers

Transformation of divergence theorem in dynamical fields
http://angelfire.lycos.com/la3/selftrans/archive/archive.html#div

Theorem of curl of a potential vector in dynamical fields
http://angelfire.lycos.com/la3/selftrans/v2_2/contents.html#curl

On gradient of potential function of dynamic field
http://angelfire.lycos.com/la3/selftrans/v4_1/contents4.html#grad

we made some progress in order to correct the standard equations for
dynamic fields, though, undoubtedly, this work is far from being done.
But we have to develop, if we want to build really universal equations
for the field, as at due time the laws for classical mechanics have
been formulated.

In this view, it seems to me very important to continue our
discussion, to draw the colleagues and to explain them in this
discussion the depth of this problem, which, as we both see, most
colleagues simply do not understand.

Thank you for this in advance,

Sergey